Answer: x = 6, x = -4
Step-by-step explanation:
Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):
0 = x² - 2x - 24
∧
1 -24
2 -12
3 -8
4 -6 = -2 This works!
0 = (x + 4)(x - 6)
Apply the Zero-Product Property (set each factor equal to zero and solve)
0 = x + 4 0 = x - 6
-4 = x 6 = x
The solutions are x = 6 and x = -4. Therefore, the zeros of the function are 6 and -4.
Finding the Zeros of the Function p(x) = x^2 – 2x – 24
To find the zeros of the function p(x) = x^2 – 2x – 24, we need to determine the values of x that make the function equal to zero. This means we solve the equation:
x^2 – 2x – 24 = 0
This is a quadratic equation and can be solved using factoring. We look for two numbers that multiply to -24 and add to -2. These numbers are 4 and -6:
(x - 6)(x + 4) = 0
Setting each factor equal to zero gives us the solutions:
x - 6 = 0 → x = 6x + 4 = 0 → x = -4So, the zeros of the function p(x) = x^2 – 2x – 24 are 6 and -4.
help simplify please choose the correct answer~!!!!!
Answer:
A
Step-by-step explanation:
Given
-4x²(5[tex]x^{4}[/tex] - 3x² + x - 2)
Multiply each term in the parenthesis by - 4x²
= - 20[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex] - 4x³ + 8x²
Answer:
A
Step-by-step explanation:
Find the sum of the roots the following equation. The subject is quadratic equations with a maximum power of two (things like a(x^3)^2 + b(x^3) + c = 0 also count as a power of two) so we have to find a way to turn this into a quadratic equation. Please help.
[tex]\left(2x\:^2-3x\right)^2+4\left(2x^2-3x\right)+3=0[/tex]
[tex]\bf (2x^2-3x)^2+4(2x^2-3x)+3=0\qquad \boxed{a=2x^2-3x}\implies a^2+4a+3=0 \\\\\\ (a+3)(a+1)=0\implies a= \begin{cases} -3\\ -1 \end{cases}\qquad \stackrel{\textit{their sum}}{-3-1\implies -4}[/tex]
Answer:
3/2
Step-by-step explanation:
(2x² − 3x)² + 4 (2x² − 3x) + 3 = 0
We can simplify this using substitution. Let's say that u = 2x² − 3x.
u² + 4u + 3 = 0
Factoring:
(u + 3)(u + 1) = 0
u = -3, u = -1
Therefore:
2x² − 3x = -3, 2x² − 3x = -1
2x² − 3x + 3 = 0, 2x² − 3x + 1 = 0
For a quadratic ax² + bx + c = 0, the sum of the roots is -b/a. So in both cases, the sum is 3/2.
For which values of P and Q does the following equation have infinitely many solutions?
Px+35=−6x+Q
[tex]\bf Px+35=-6x+Q\implies \stackrel{P}{~~\begin{matrix} -6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}x+35=~~\begin{matrix} -6x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+\stackrel{Q}{35}\implies 35=35[/tex]
whenever you get an equality like so, that's a flat that both equations are exactly one and the same and thus the system has "infinitely many solutions".
A man earns a base salary of 2000$ and every year he got araise of 7% on his total income.huv much total income would he get by end of 4 years
Answer:
his total income by the end of 4 years will be: $2622.
Step-by-step explanation:
A man earns a base salary of $2000, and every year he got a raise of 7% on his total income.
The first year, he will earn: 1.07($2000) = $2140
The second year he will earn: 1.07($2140) = $2289.8
The third year he will earn: 1.07($2289.8) = $2450.086
The fourth year he will earn: 1.07($2450.086) = $2621.59202
Therefore, his total income by the end of 4 years will be: $2622.

Which best describes the transformation from the graph of f(x) = x2 to the graph of
f(x) = (x – 3)2 – 1?
left 3 units, down 1 unit
left 3 units, up 1 unit
right 3 units, down 1 unit
right 3 units, up 1 unit
Answer: Third option.
Step-by-step explanation:
These are some transformations for a function f(x):
If [tex]f(x)-k[/tex], then the function is shifted down "k" units.
If [tex]f(x-k)[/tex], then the function is shifted right "k" units.
Knowing this we can describe the transformation from the graph of the function [tex]f(x) = x^2[/tex] to the graph of the function [tex]f(x) = (x - 3)^2-1[/tex]. This is:
The function [tex]f(x) = (x - 3)^2-1[/tex] is the function [tex]f(x) = x^2[/tex] but shifted right 3 units and shifted down 1 units.
Therefore, the correct option is the third one.
Answer:
right 3 units, down 1 unit
Using the given points, determine the delta symbol y. (-3,-5) and (0,10)
Answer:
Δy = 15
Step-by-step explanation:
Δy represents the change in the y-coordinates
We are given points (-3,-5) and (0,10)
here y₁ = -5 and y₂ = 10
so, delta y will be
Δy = y₂ - y₁
Δy = 10 -(-5)
Δy = 10 + 5
Δy = 15
So, delta y Δy =15
PLEASE HELP ME SUPER FAST IM STICK ON THESE 3!
See attachment below!
Answer:
25. The area of the trapezoid is 96 cm² ⇒ 2nd answer
26. The area of the kite is 40.8 feet² ⇒ 3rd answer
31. The area of the circle is 6.0025π m² ⇒ 3rd answer
Step-by-step explanation:
* Lets solve the problems
25. The figure is trapezoid
- The trapezoid has two parallel bases base 1 and base 2
- The area of the trapezoid is 1/2(base 1 + base 2) × height
- The length of base 1 is 12 cm
- The length of its height is 6 cm
- The length of the base 2 is (2 + 12 + the adjacent side to ∠45°)
- To find the missing part in the base 2 use the trigonometry
function tan 45° = opposite/adjacent
∵ tan 45° = opposite/adjacent
∵ The opposite = 6
∵ tan 45° = 1
∴ 1 = 6/adjacent ⇒ by using cross multiplication
∴ The adjacent = 6 cm
∴ The length of base 2 = 2 + 12 + 6 = 20 cm
∵ The area of the trapezoid is 1/2(base 1 + base 2) × height
∵ The length of base 1 = 12 cm
∵ The length of base 2 = 20 cm
∵ The length of its height = 6 cm
∴ The area = 1/2(12 + 20) × 6 = 1/2(32) × 6 = 16 × 6 = 96 cm²
* The area of the trapezoid is 96 cm²
26. The figure is kite
- The kite has two diagonals
- Its diagonals perpendicular to each other
- The longest diagonal bisects the shortest diagonal
- The area of the kite is 1/2(diagonal 1 × diagonal 2)
∵ The length of diagonal 1 = 10.2 feet
∵ The length of diagonal 2 = 8 feet
∵ The area of the kite = 1/2(diagonal 1 × diagonal 2)
∴ The area = 1/2(10.2 × 8) = 1/2(81.6) = 40.8 feet²
* The area of the kite is 40.8 feet²
31. The figure is a circle
- The circle has diameter
- The radius is half the diameter
- The area of the circle is π r²
∵ The length of the diameter = 4.9 m
∵ The length of the radius 1/2 the length of the diameter
∴ The length of the radius = 1/2 (4.9) = 2.45 m
∵ The area of the circle = π r²
∴ The area = π (2.45)² = 6.0025π m²
* The area of the circle is 6.0025π m²
Answer:
25) 96 cm²
26) 40.8 ft ²
31). 6.0025π m²
Step-by-step explanation:
25) To find the area of trapezoid
Area of trapezoid = h(a + b)/2
Here a = 6 + 12 + 2 = 20 cm
b = 12 cm and h = 6
Area = h(a + b)/2
= 6(20 + 12)/2
= 96 cm²
26) To find the area of kite
Area of kite = pq/2
Where p and q are the two diagonals
Here p = 10.2 ft and q = 8 ft
Area = pq/2
= (10.2 * 8)/2 = 40.8 ft²
31) To find the area of circle
Area of circle = πr²
Here r = 4.9/2 = 2.45 m
Area = πr²
= π *(2.45)²
= 6.0025π m²
I really dont get this and I really need to get past it help me please
Answer:
26
Step-by-step explanation:
Area of a triangle is:
A = 1/2 b h
Given b = 13 and h = 4:
A = 1/2 (13 cm) (4 cm)
A = 26 cm²
Evaluate the following expression for d=-5 and w=6
[tex] \frac{d {}^{0} }{w {}^{ - 3} } [/tex]
A. -23
B. 1/216
C. 216
D. -18
Answer:
216
Step-by-step explanation:
Anything to the zero power is equal to 0.
The denominator can be moved to the numerator because the exponent is negative. So it is now 1*6^3. This is equal to 216.
The value of expression [tex]\frac{d^{0} }{w^{-3} }[/tex] is 216
The correct option is (B).
What is exponents and power?Power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.
Given:
[tex]\frac{d^{0} }{w^{-3} }[/tex]
put d=-5 and w=6
So, [tex]\frac{-5^{0} }{6^{-3} }[/tex]
=1/[tex]6^{-3}[/tex] [a°=1]
=6³ [[tex]1/a^{-b} = a^{b}[/tex]]
=216.
hence, [tex]\frac{d^{0} }{w^{-3} }[/tex] = 216.
Learn more about exponents and power here:
https://brainly.com/question/15722035
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you are recreating a scale drawing at a different scale. The orginal scale is 1 cm : 4m The new scale is 1cm : 2cm. In the original drawing, the length of a segment is 7 cm. How long should the segment represnting the same distanc be in the new drawing?
Answer:
14 cm
Step-by-step explanation:
step 1
Find the actual length of the segment
we know that
The original scale is 1 cm : 4m
In the original drawing, the length of a segment is 7 cm
therefore
Let
x ----> the actual length of the segment
by proportion
1/4=7/x
x=4*7
x=28 m
step 2
Find the length of the segment in the new drawing
The new scale is 1cm : 2m
Let
x ---> the length of the segment in the new drawing
by proportion
Remember that
The actual length is 28 m
1/2=x/28
x=28/2
x=14 cm
A rock dropped on the moon will increase its speed from 0 m/s (its starting
speed) to 8.15 m/s in about 5 seconds. If you were standing on the moon,
measuring the rock's motion, what would you measure for the magnitude of
its acceleration?
O
A. 8.2 m/s2
O B. 41 m/s2
O C. 9.8 m/s2
O D. 1.63 m/s2
The answer is:
The correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Why?To calculate the acceleration, we need to use the following formula that involves the given information (initial speed, final speed, and time).
We need to use the following free fall equation:
[tex]V_{f}=V_{o}-g*t[/tex]
Where:
[tex]V_{f}[/tex] is the final speed.
[tex]V_{o}[/tex] is the initial speed.
g is the acceleration due to gravity.
t is the time.
We are given the following information:
[tex]V_{f}=8.15\frac{m}{s}[/tex]
[tex]V_{o}=0\frac{m}{s}[/tex]
[tex]t=5seconds[/tex]
Then, using the formula to isolate the acceleration, we have:
[tex]V_{f}=V_{o}-g*t[/tex]
[tex]V_{f}=V_{o}-g*t\\\\g*t=V_{o}-V_{f}\\\\g=\frac{V_{o}-V_{f}}{t}[/tex]
Now, substituting we have:
[tex]g=\frac{V_{o}-V_{f}}{t}[/tex]
[tex]g=\frac{0-8.15\frac{m}{s}}{5seconds}=-1.63\frac{m}{s^{2}}[/tex]
Therefore, since we are looking for a magnitude, we have that the obtained value will be positive, so:
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Hence, the correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Have a nice day!
Write the linear Inequality shown in the graph. The gray area represents the shaded region.
ANSWER
[tex]y \leqslant - x + 4[/tex]
EXPLANATION
The equation of the boundary line is
[tex]y = - x + 4[/tex]
Hence the inequality is either
[tex]y \leqslant - x + 4[/tex]
or
[tex]y \geqslant - x + 4[/tex]
We test the origin to get determine which one represents the shaded
We substitute (0,0) into the first inequality to get;
[tex]0\leqslant - (0) + 4[/tex]
This implies that,
[tex]0 \leqslant 4[/tex]
Hence the correct answer is
[tex]y \leqslant - x + 4[/tex]
Answer: Second Option
[tex]y \leq -x +4[/tex]
Step-by-step explanation:
The region is bounded by a line of negative slope that cuts the y-axis at the point y = 4 and cuts the x-axis at the point x = 4.
So the equation of this line is
[tex]y = -x + 4[/tex]
If the region is composed of all the points that lie below the line y = -x + 4 then it means that the region is formed by all the values of y less than or equal to the line [tex]-x + 4[/tex].
Therefore the inequation is:
[tex]y \leq -x +4[/tex]
Second Option
The volume of a cube is 27n27 cubic units. What is the lenth of one side of the cube?
Answer: B . on your test
Step-by-step explanation:
Which expression is a perfect cube?
A. x8
B. y24
C. m28
D. x64
Answer:
B. Y²⁴
Step-by-step explanation:
For perfect cubes, the exponents are a multiple of three. If yᵃ is a perfect cube, then a/3=k where k is a whole number.
Among the provided choices, the exponent of y²⁴ is divisible by 3.
24/3 = 8.
Thus y²⁴ is a perfect cube.
Answer:
B
thats the answer on edge 2020
There are 85 apples on the big tree, John picked out 15%. How many did John pick out?
Answer:
12.75
Step-by-step explanation:
John picked out 12.75 apples on the big tree.
15% of 85 is 12.75.
Hope this helps! Please mark brainliest!
Answer:
approx 13 apples
Step-by-step explanation:
total apples : 85
given john picked 15% = 0.15 of the total apples
number of apples john picked = 0.15 x 85 = 12.75
rounding off to nearest whole number (because you can't really pick 0.75 of an apple) = 13 apples
Solve the system of equations. 4x + 2y = –14 6x + 3y = –22 (0, –7), (–1, –6), no solutions, infinitely many solutions. Plz and Thank You
Answer:
no solutions
Step-by-step explanation:
4x + 2y = –14
6x + 3y = –22
Divide the first equation by 2 and the second equation by 3
4x/2 + 2y/2 = –14/2 2x +y = -7
6x/3 + 3y/3 = –22/3 2x + y = -22/3
The left hand sides are the same but the right hand sides are different.
Multiply the second equation by -1
2x+y = -7
-2x -y = 22/3
-------------------
0 = -7+22/3
0 = 1/3
This is never true, so there are no solutions
Answer:
B, No Solutions
Step-by-step explanation:
MARKING BRAINLIEST!
Given that DMKT → FCBN, what is m B?
Answer:
79°
Step-by-step explanation:
given both figures are congruent, and one is simply a rotation of another
m∠B corresponds to m∠k = 79°
Answer:
Given that DMKT → FCBN, B is 79°
Step-by-step explanation:
m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N
m∠K = 79° therefore m∠B = 79°.
Please mark brainliest and have a great day!
The circle below is centered at (3 1) and has a radius of 2 what is its equation
Answer:
(x-3)^2 + (y-1)^2 = 4
Step-by-step explanation:
The equation of a circle is usually written in the form
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r is the radius
The center is at the origin so (h,k) = (3,1) and the radius is 2 so r=2
(x-3)^2 + (y-1)^2 = 2^2
(x-3)^2 + (y-1)^2 = 4
plz answer How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
Two solutions
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
Both lines have a slope m = - [tex]\frac{1}{2}[/tex]
Hence the lines are parallel and have no points of intersection
Thus the system has no solution → A
One box of clips weighs 4 2/3 ounces. Another box weighs 5 3/8 ounces. What is the total weight of the two boxes?
For this case, we convert the mixed numbers to fractions:
Box 1: [tex]4 \frac {2} {3} = \frac {3 * 4 + 2} {3} = \frac {14} {3}[/tex]
Box 2: [tex]5 \frac {3} {8} = \frac {8 * 5 + 3} {8} = \frac {43} {8}[/tex]
We add the fractions to find the total weight of the boxes:
[tex]\frac {14} {3} + \frac {43} {8} = \frac {8 * 14 + 43 * 4} {3 * 8} = \frac {112 + 172} {24} = \frac {284 } {24} = \frac {142} {12} = \frac {71} {6}[/tex]
Thus, between the two boxes weigh[tex]\frac {71} {6}[/tex] ounces.
In mixed number: [tex]11 \frac {5} {6}[/tex]
Answer:
[tex]11 \frac {5} {6}[/tex]ounces
The total weight of the two boxes is 10 1/24 ounces, found by converting the mixed numbers into improper fractions, finding a common denominator, and adding the fractions together.
Explanation:To find the total weight of two boxes when one weighs 4 2/3 ounces and the other weighs 5 3/8 ounces, we first convert the mixed numbers into improper fractions. For 4 2/3 ounces, this would be (4 × 3) + 2 = 14/3 ounces. For 5 3/8 ounces, it is (5 × 8) + 3 = 43/8 ounces. Once in improper fraction form, we find a common denominator, which is 24, and then we add the two fractions together.
The first box in twenty-fourths is (14/3) × (8/8) = 112/24. The second box is (43/8) × (3/3) = 129/24. Adding them gives us 112/24 + 129/24 = 241/24. We divide 241 by 24, which results in 10 with a remainder of 1, giving us 10 1/24 ounces.
Therefore, the total weight of the two boxes is 10 1/24 ounces.
Find y if the line through (1,y) and (5,7) has a slope of 6.
Let FGHB a right triangle with right angle G and an altitude as shown find XYZ
Answer:
Part 1) [tex]z=4\sqrt{2}\ units[/tex]
Part 2) [tex]x=18\ units[/tex]
Part 3) [tex]y=12\sqrt{2}\ units[/tex]
Step-by-step explanation:
step 1
Find the value of z
In the smaller right triangle IFG of the figure
Applying the Pythagoras Theorem
[tex]6^{2}=2^{2}+z^{2}[/tex]
[tex]z^{2}=6^{2}-2^{2}[/tex]
[tex]z^{2}=32[/tex]
[tex]z=4\sqrt{2}\ units[/tex]
step 2
In the right triangle HFG
Applying the Pythagoras Theorem
[tex]x^{2}=y^{2}+6^{2}[/tex]
[tex]y^{2}=x^{2}-36[/tex] -----> equation A
step 3
In the right triangle HIG
Applying the Pythagoras Theorem
[tex]y^{2}=z^{2}+(x-2)^{2}[/tex]
[tex]y^{2}=32+(x-2)^{2}[/tex] -----> equation B
step 4
equate equation A and equation B
[tex]x^{2}-36=32+(x-2)^{2}\\x^{2}-36=32+x^{2}-4x+4\\4x=36+36\\4x=72\\x=18\ units[/tex]
step 5
Find the value of y
Substitute the value of x in the equation B
we have
[tex]x=18\ units[/tex]
[tex]y^{2}=32+(18-2)^{2}[/tex]
[tex]y^{2}=32+(16)^{2}[/tex]
[tex]y^{2}=288[/tex]
[tex]y=12\sqrt{2}\ units[/tex]
Rewrite the quadratic function in vertex form. Then, determine the maximum or minimum and the axis of symmetry.
y = -3x 2 + 18x - 2
Answer:
See below in BOLD.
Step-by-step explanation:
y = -3x 2 + 18x - 2
y = -3(x^2 - 6x) - 2
y = -3 [ (x - 3)^2 - 9] - 2
y = -3(x - 3)^2 + 25 is vertex form.
The coefficient of x^2 is negative so we have a maximum value of the function.
The maximum value is 25 and the axis of symmetry is x = 3.
Answer: The maximum value is 25 and the axis of symmetry is x = 3.
Solve the system of equations. 2x+2y+3z=5, 6x+3y+6z=6 and 3x+4y+4z=9
Answer:
it's d or the fourth option
Step-by-step explanation:
write a function rule for the output is 5 less than the input
Answer:
y=x-5
Step-by-step explanation:
"output" means y
and "input" means x
So all you need to find is the =
Please mark brainliest and have a great day!
(07.09) Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is c(p) = 0.85p, where p is the original price of the car. He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is f(c) = 1.09c, where c is the sale price of the car. Determine the composite function that can be used to calculate the final price of Jonah's car by solving for f[c(p)]. (1 point) f[c(p)] = 0.9265cp f[c(p)] = 0.9265p f[c(p)] = 1.94cp f[c(p)] = 1.94p
Answer:
Answer: f[c(p)] = 0.9265p
Step-by-step explanation:
Given: Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is , where p is the original price of the car.
He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is , where c is the sale price of the car.
Now, the composite function that can be used to calculate the final price of Jonah's car is given by :-
Answer:
f[c(p)] = 0.9265p
Step-by-step explanation:
c(p) = 0.85p
f(c) = 1.09c
f[c(p)] = f[0.85p] = 1.09(0.85p) = 0.9265p
Answer: f[c(p)] = 0.9265p
A population numbers 508 organisms initially and increases by 6.2% each year.
Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.
To find the population after t number of years, multiply the starting population by 1 plus the percent increase raised to the number of years.
The equation would be: P = 508(1.062)^t
Teresa is on her way home in her car. Her drive is 6miles long. She has finished two-thirds of the drive so far. How far has she driven?
Answer:
4 miles
Step-by-step explanation:
6 divided by 3 = 2 = one-third of 6
--> multiply by two to get two thirds of six = 4 miles
Answer:
4 miles
Step-by-step explanation:
Sparkles the unicorn is in the forest. She is helping herself to a nice big juicy apple. The monkey grabs the apple out of her mouth and starts to eat it. Sparkles notices that there are 18 pairs of eyes staring at the monkey. Based on the information you have been given, how many animals are in the forest in this moment?
Answer:
11 animals
Explanation:
-Sparkles is the first animal that is introduced, then the monkey is the second. Since there are 18 eyes, that can be divided by 2 to tell you how many of the remaining animals there are. Which would lead up to 9 and 9+2=11
Eleven (11) Animals
Based on the above given information, it can be construed that that Eleven (11) animals are in the forest.
Further ExplanationThe first mentioned animal is Sparkles the Unicorn (Animal 1) who probably might be hungry and, might have searched through the forest to get the nice big juicy apple.
She might have dodged several wild predating animals just for luck to smile on her through the discovery of a big juice apple. She plucks it, and starts eating. A nearby lurking, cunning monkey (Animal 2), snatches the fruit from Sparkles the Unicorn, due to her carelessness, and as she proceed to retrieve the fruit, she discovered that that wasn’t the only monkey around. She sees eighteen (18) pairs of eyes which means, there are nine (9) other animals i.e. 18 pairs of eyes divided by 2 (18/2 = 9) are also in the forest.
Therefore:
Animal 1 + Animal 2 + 9 other Animals = 11 Animals
This kind of question can be said to be a Mathematical Puzzle.
Mathematical puzzle is a form of recreational mathematics, which helps to enhance students’ knowledge.
Mathematical puzzle helps students to understand different concepts of mathematical problems.
This form of mathematical improve students’ learning ability
KEYWORDS:
forestpuzzleanimalwildstudentsA runner can run at 7.5 miles per hour. Write an equation that compares the time (t) with the distance (d).
Answer:
d = 7.5t
Step-by-step explanation:
t = time
d= distance
you want to write an equation that compares time with distance.
in the question it says per hour whoch means 7.5 miles have been ran each hour. however we dont know how mmany hour lets say tom has ran. therefore, we use t instead. we got d to go behind the = sign because we are comparing. When we multiply 7.5t we are going to get the distance he ran, d.
hope this helps!
Answer:
d=7.5t
Step-by-step explanation: